GLP-1 receptor agonists - How weight loss injections work

Anti-obesity drugs, also known as obesity drugs or GLP-1 receptor agonists have been made popular by celebrities using them to lose substantial amounts of weight. But how do these therapeutics work and are there downsides to taking them?
References:
great summary, short article: www.nature.com...
1 Zhang et al.: pubmed.ncbi.nl...
2 Wilding et al.: pubmed.ncbi.nl...
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[@vanesslifeygo]

Would the synthetic version down regulate your own production of GLP-1?

[@blahsomethingclever]

Some plants contain natural appetite suppressors that work on this receptor, I'm sure. Eating certain wild leafy greens seems to have an immediate and immense effect on appetite suppression.
Stinging nettle comes to mind.